I'm pretty sure he's saying the guy/gal working from home with 4 kids running around can't be a productive employee. Which is probably true for most cases. Kids can be a giant distraction.
Kids can be a distraction, for sure. Just like coworkers or officemates who frequently disrupt others (even if not directly, such as the cube next to someone trying to concentrate).
When at home, if I feel the a distraction looming, it's easy to shut the door. Problem (mostly) solved.
When the poster says "maintaining", I'm guessing the employee was doing double-duty as a stay-at-home mom/dad, at which point you can't always just shut the door for 8 hours.
You're 100% correct if that is the meaning. But, that isn't "working" full time (unless it was a pre-agreed arrangement). That shouldn't be allowed, but poor management will not catch/act on it.
However, I was specifically replying to the context of having distractions (kids, in this case) in gcp's and alistairSH's comments.